This seems like a lazy way to enhance performance. And...it is baseball. Not like they are athletes or anything! (ducks)
That was just a snarky, joking way of saying: if he were a long distance runner, a swimmer, a wrestler, or even a football player, I might be able to see the perceived benefit. If a golfer told me they did this as a way to enhance their game, I would wonder what part of their game they are enhancing...the ability to walk from hole to hole? Same for baseball. It isn't considered to be a high-endurance sport.
Plus, if he is doing this in the off-season, what kind of benefit does that give to his in-season performance? I cannot imagine this has effects that last more than weeks to months at at time post procedure.
But, in the end...it IS his own money (and his own blood) so...he and his money may be parted, and he thinks he gets something out of it.
Performance can be related to health in ways that are regardless of how much an athlete “stays in shape and trains”. Or even that “plus eats properly and well”.
If filtering the blood and oxygenating it gives a boost to how well the internal body systems are working, I can see it enhancing athletic performance as well - like with energy and stamina with internal systems that are performing better.